This week I'm going to start running a Beginner's Box campaign at a friend's game store. The plan is for it to be open to both regular players and drop-in players. This means that after a month or two, I should expect to have player-characters with a range of levels showing up on a given night.

I have some experience GMing Pathfinder Society games, but have yet to GM a Beginner Box game for any characters other than the pregens. Also, this is my first time designing encounters for Beginner Box. The Challenge Rating system in the GM Guide looks similar to the system in the full game, but it appears that adding monsters to an encounter gives a different CR result in Beginner Box than it would in Pathfinder.

For example, in Beginner Box an encounter with 3 CR 1/2 giant centipedes is considered a CR 2 encounter, while in the full game it would be a CR 3 encounter.

For the first few sessions, I am more concerned about balancing encounters based on party size than level, since everyone will be level 1. My plan is simply to add additional monsters as needed. But, once the regular players hit levels 3-4, adding monsters makes it more likely that any level 1 characters will be killed.

Has anybody run a Beginner Box game with characters of different levels? And if so, how did you go about balancing the encounters?

I would advise against having PCs of different levels; besides the balancing reasons you gave, it also lets whoever isn't a higher level sit there and not really be able to participate meaningfully. When it's time to level just let everyone level and stay on the same page.